Finite Group Databasebeta

← #25140960

Subgroups — #25140960

Order 11008.

834 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138908C211yesmaximal, characteristic
2#19137491C211yesmaximal, characteristic
3#19136156C211yesmaximal, characteristic, complemented
4#19136075C211yesmaximal, characteristic, complemented
5#19136031C211yesmaximal, characteristic, complemented
6#19135182C211yesmaximal, characteristic, complemented
7#19135179C211yesmaximal, characteristic, complemented
8#19134884C211yesmaximal, characteristic
9#19134790C211yesmaximal, characteristic, complemented
10#19134789C211yesmaximal, characteristic, complemented
11#19134684C211yesmaximal, characteristic, complemented
12#19134679C211yesmaximal, characteristic, complemented
13#19134617C211yesmaximal, characteristic, complemented
14#340×D43C211yesmaximal, characteristic, complemented
15C43×#2077C211yesmaximal, characteristic, complemented
16C22×C8×D43C2211yescharacteristic
17C2×C4×C22⋊D43C2211yescharacteristic
18C2×(C22⋊D43)⋊C4—21no—
19C22×C4⋊Dic43C2211yescharacteristic
20C2×C4⋊C4×D43C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×C22⋊(C43⋊C8)C2211yescharacteristic
26C2×(C2×D43)⋊C8C2211yescharacteristic
27#14582840—21no—
28#14582835—21no—
29#14582798C2211yescharacteristic
30#14582796—21no—
31#14582795C2211yescharacteristic
32#14582775—21no—
33#14582773—21no—
34#14582773—21no—
35#14582771—21no—
36#14582768C2211yescharacteristic
37#14582759C2211yescharacteristic
38#14582756C2211yescharacteristic
39#14582756C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41#14582662C2211yescharacteristic
42#14582662C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C2×C22⋊C8×C43C2211yescharacteristic
54C43×#380C2211yescharacteristic
55C43×#380C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×C22⋊D43D411yescharacteristic
60C23×Dic43—21no—
61C22×C4×D43—21no—
62C22×C4×D43—21no—
63C22×C4×D43C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C2×C8×D43—22no—
67C2×C8×D43—22no—
68C2×C8×D43—41no—
69C4×C22⋊D43—22no—
70C4×C22⋊D43—22no—
71(C22⋊D43)⋊C4—44no—
72C2×C4⋊Dic43—22no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—41no—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4D411yescharacteristic
86C4⋊C4×D43—22no—
87C4⋊C4×D43—22no—
88C4⋊C4×D43—22no—
89C4⋊C4×D43—41no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43D411yescharacteristic
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4D411yescharacteristic
95C2×C4×Dic43—21no—
96C2×C4×Dic43C2311yescharacteristic
97#13063257—22no—
98#13063257—41no—
99#13063256—41no—
100C22⋊(C43⋊C8)—41no—
101(C2×D43)⋊C8—22no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C23×C4×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117#106×C43—22no—
118C22⋊C8×C43—22no—
119#95×C43—21no—
120#95×C43—21no—
121C24×C43C2×D411yescharacteristic
122C23×D43C2×D411yescharacteristic
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2411yescharacteristic
135C2×C22⋊D43—22no—
136C2×C22⋊D43—22no—
137C2×C22⋊D43SD1614yes—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—42no—
143C22×Dic43—42no—
144C22×Dic43—81no—
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C2×C4×D43—21no—
149C2×C4×D43—21no—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—42no—
153C2×C4×D43—42no—
154C2×C4×D43—42no—
155C2×C4×D43—81no—
156C2×C4×D43—81no—
157C2×C4×D43—81no—
158C2×C4×D43#4112yes—
159C2×C4×D43#4112yes—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43#4112yes—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C22⋊C4×C43—42no—
175C22⋊C4×C43—81no—
176C22⋊Dic43—22no—
177C22⋊Dic43—81no—
178(C2×D43)⋊C4—22no—
179(C2×D43)⋊C4—42no—
180(C2×D43)⋊C4—42no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—42no—
189C4⋊Dic43—81no—
190C4⋊Dic43#4112yes—
191Dic43⋊C4—22no—
192Dic43⋊C4—42no—
193Dic43⋊C4—42no—
194Dic43⋊C4—42no—
195Dic43⋊C4—81no—
196Dic43⋊C4—81no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—42no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C8×D43—44no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43C2×SD1612yes—
214C23×C43C22×D411yescharacteristic
215C22×D43—21no—
216C22×D43—21no—
217C22×D43—21no—
218C22×D43—21no—
219C22×D43#12312yes—
220C22×D43C2×SD1612yes—
221C22×D43#13712yes—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43H(5,𝔽2)11yescharacteristic
246C2×C4×C432−1+411yescharacteristic
247C22⋊D43—28no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—22no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—84no—
268C2×Dic43#12312yes—
269C2×Dic43C2×SD1612yes—
270C4×D43—22no—
271C4×D43—22no—
272C4×D43—22no—
273C4×D43—22no—
274C4×D43—84no—
275C4×D43—84no—
276C8×C43—22no—
277C8×C43—41no—
278C43⋊C8—41no—
279C43⋊C8—41no—
280#24935—431nomaximal, Sylow
281C22×C43—22no—
282C22×C43—22no—
283C22×C43—22no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43C2×#12311yescharacteristic
289C22×C43#54611yescharacteristic
290C22×C43#54711yescharacteristic
291C22×C43C22×SD1611yescharacteristic
292C22×C43C2×#13711yescharacteristic
293C22×C43#57611yescharacteristic
294C22×C43#57711yescharacteristic
295C2×D43—22no—
296C2×D43—22no—
297C2×D43—22no—
298C2×D43—22no—
299C2×D43—22no—
300C2×D43—22no—
301C2×D43#48314yes—
302C4×C43—41no—
303C4×C43—81no—
304C4×C43—81no—
305C4×C43—81no—
306C4×C43—81no—
307C4×C43#52911yescharacteristic
308C4×C43#53911yescharacteristic
309C4×C43#55111yescharacteristic
310C4×C43#55211yescharacteristic
311Dic43—22no—
312Dic43—22no—
313Dic43—41no—
314Dic43—42no—
315Dic43—81no—
316Dic43—81no—
317Dic43—81no—
318#2487—431no—
319D4×C4⋊C4—431no—
320#2099—431no—
321#2084—431no—
322#2077—431no—
323#2077D4311yescharacteristic, complemented
324#1920—431no—
325#1920—431no—
326#1869—431no—
327#1853—431no—
328#1853—431no—
329#1824—431no—
330#1823—431no—
331#1807—431no—
332C2×#340—431no—
333C2×C43—42no—
334C2×C43#241911yescharacteristic
335C2×C43C2×#48311yescharacteristic
336C2×C43#309611yescharacteristic
337C2×C43#329511yescharacteristic
338C2×C43#332011yescharacteristic
339C2×C43#333511yescharacteristic
340C2×C43#334611yescharacteristic
341D43—24no—
342C23×C8—431no—
343C2×C4×D4—431no—
344C2×C4×D4—861no—
345C22×C4⋊C4—431no—
346C22×C4⋊C4—431no—
347C22×C4⋊C4—431no—
348C2×#106—431no—
349C2×#106—431no—
350C2×#106—431no—
351C2×#106C2×D4311yescharacteristic
352C2×C22⋊C8—431no—
353C2×C22⋊C8—431no—
354C2×C22⋊C8C2×D4311yescharacteristic
355#400—861no—
356#399—861no—
357#389—431no—
358#389—431no—
359#389—861no—
360#386—861no—
361#385—861no—
362#385—861no—
363#385—861no—
364#384—431no—
365#380—431no—
366#380—431no—
367#380—431no—
368#380C2×D4311yescharacteristic
369#380C2×D4311yescharacteristic
370C4×C4⋊C4—431no—
371#340—431no—
372#340—431no—
373#340—431no—
374#340—431no—
375#340—431no—
376#340—431no—
377#340—431no—
378#340—431no—
379#340—431no—
380#340C2×D4311yescharacteristic
381#340C2×D4311yescharacteristic
382#340C2×D4311yescharacteristic
383#336—431no—
384#336—431no—
385C43#2493511yescharacteristic, complemented, Sylow
386C22×D4—431no—
387C23×C4—431no—
388C23×C4—861no—
389C23×C4—861no—
390C23×C4—861no—
391C23×C4C22×D4311yescharacteristic
392C22×C8—431no—
393C22×C8—431no—
394C22×C8—862no—
395C22×C8—862no—
396C22×C8—1721no—
397C22×C8C22×D4311yescharacteristic
398C22×C8C22×D4311yescharacteristic
399C4×D4—862no—
400C4×D4—862no—
401C4×D4—1724no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—862no—
408C2×C4⋊C4—862no—
409C2×C4⋊C4—862no—
410C2×C4⋊C4—862no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—1721no—
419C2×C4⋊C4—1721no—
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C4⋊C4C22×D4311yescharacteristic
423C2×C4⋊C4C22×D4311yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—431no—
427C2×C22⋊C4—431no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C42—431no—
432C2×C42—861no—
433#106—22no—
434#106—862no—
435#106—1721no—
436#106—1721no—
437C22⋊C8—22no—
438C22⋊C8—862no—
439C22⋊C8—1721no—
440#95—21no—
441#95—21no—
442#95—861no—
443#95—861no—
444#95—861no—
445#95—861no—
446#95—861no—
447#95—861no—
448C24—431no—
449C24D4×D4311yescharacteristic
450C2×D4—434no—
451C2×D4—862no—
452C2×D4—862no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—431no—
464C22×C4—431no—
465C22×C4—432no—
466C22×C4—432no—
467C22×C4—431no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—3441no—
477C22×C4—3441no—
478C22×C4—3441no—
479C22×C4—3441no—
480C22×C4—1722no—
481C22×C4—1722no—
482C22×C4—1722no—
483C22×C4—1722no—
484C22×C4—1722no—
485C22×C4D4×D4311yescharacteristic
486C22×C4C23×D4311yescharacteristic
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—1724no—
499C2×C8#1062190012yes—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—432no—
509C4⋊C4—862no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—3441no—
518C4⋊C4—3441no—
519C4⋊C4—3441no—
520C4⋊C4—1722no—
521C4⋊C4—1722no—
522C4⋊C4—1722no—
523C4⋊C4—1722no—
524C22⋊C4—42no—
525C22⋊C4—81no—
526C22⋊C4—862no—
527C22⋊C4—862no—
528C22⋊C4—3441no—
529C22⋊C4—1722no—
530C22⋊C4—1722no—
531C42—861no—
532C42—861no—
533C42—1722no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—432no—
541C23—432no—
542C23—432no—
543C23—861no—
544C23—861no—
545C23—861no—
546C23—861no—
547C23SD16×D4312yes—
548C23C2×D4×D4311yescharacteristic
549D4—868no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—432no—
570C2×C4—432no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—862no—
576C2×C4—862no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—862no—
583C2×C4—3444no—
584C2×C4—3444no—
585C2×C4—3444no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4#41×D4311yescharacteristic
598C2×C4#41×D4311yescharacteristic
599C2×C4#41×D4311yescharacteristic
600C2×C4C2×#1062190011yescharacteristic
601C2×C4#1306337111yescharacteristic
602C2×C4#1306337211yescharacteristic
603C8—22no—
604C8—41no—
605C8—1721no—
606C8—1721no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—434no—
615C22—862no—
616C22—862no—
617C22—862no—
618C22—862no—
619C22—862no—
620C22—862no—
621C22#123×D4311yescharacteristic
622C22#1458354111yescharacteristic
623C22#1458354911yescharacteristic
624C22C2×SD16×D4311yescharacteristic
625C22#137×D4311yescharacteristic
626C22#1458370311yescharacteristic
627C22#1458370611yescharacteristic
628C4—41no—
629C4—81no—
630C4—81no—
631C4—81no—
632C4—81no—
633C4—862no—
634C4—862no—
635C4—3441no—
636C4—3441no—
637C4—3441no—
638C4—1721no—
639C4—1722no—
640C4#1458342811yescharacteristic
641C4#1458349011yescharacteristic
642C4#1458357211yescharacteristic
643C4#1458358511yescharacteristic
644C2—42no—
645C2—864no—
646C2#1913806511yescharacteristic
647C2#483×D4311yescharacteristic
648C2#1914454811yescharacteristic
649C2#1914641711yescharacteristic
650C2#1914676911yescharacteristic
651C2#1914694711yescharacteristic
652C2#1914707511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2077C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenter#2077D43
hypocenterC43#24935
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2077

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #19136156C2semidirect
4. #19136075C2semidirect
5. #19136031C2semidirect
6. #19135182C2semidirect
7. #19135179C2semidirect
9. #19134790C2semidirect
10. #19134789C2semidirect
11. #19134684C2semidirect
12. #19134679C2semidirect
13. #19134617C2semidirect
14. #340×D43C2semidirect
15. C43×#2077C2semidirect
323. #2077D43semidirect
385. C43#24935semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191389082
#191374912
#191361562
#191360752
#191360312
#191351822
#191351792
#191348842
#191347902
#191347892
#191346842
#191346792
#191346172
#340×D432
C43×#20772
#2493543